Thank you for commenting sir.
The problem is tricky a little bit.
Let me give you a hint:
Consider ABCD is cyclic quadrilateral whose center is at point B. Try using circum- circle property of a quad. AB,BD and BC will be the radius of the circle. Hence BD=10 cm.
Interesting but how are we suppose to know that it was a cyclical quadrilateral? Without that information there are various quadrilaterals that meet the length and angle measurements of the image you provided.
Geometry : central angle is twice the angle on the circumference